Question

数学 公式法 因式分解

1.4(x+y+z)^2-9(x-y-z)^2
2.2a^(a^2-25b^2)+50b^2(25b^2-a^2)
3.32a(x^2+2x)^2-2a
4.-x^n+4 +81x^n(y-z)^2
5.100乘14.5^2-100乘5.5^2
6.788^2-212^2除500

Answer 1

因式分解：公式法.能合并的同类项要合并

Answer 2

1.4(x+y+z)^2-9(x-y-z)^2
=[2(x+y+z)]^2-[3(x-y-z)]^2
=(2x+2y+2z)^2-(3x-3y-3z)^2
=[(2x+2y+2z)+(3x-3y-3z)][(2x+2y+2z)-(3x-3y-3z)]
=(5x-y-z)(5y+5z-x)

2.2a^2(a^2-25b^2)+50b^2(25b^2-a^2)
=2a^2(a^2-25b^2)-50b^2(a^2-25b^2)
=2(a^2-25b^2)^2
=2(a+5b)^2(a-5b)^2

3.32a(x^2+2x)^2-2a
=2a[16(x^2+2x)^2-1]
=2a(4x^2+8x+1)(4x^2+8x-1)

4.-x^(n+4) +81x^n(y-z)^2
=-x^n[x^4-81(y-z)^2]
=-x^n(x^2+9y-9z)(x^2-9y+9z)

5.100×14.5^2-100×5.5^2
=100×(14.5^2-5.5^2)
=100×(14.5+5.5)×(14.5-5.5)
=100×20×9
=18000

6.(788^2-212^2)÷500
=(788+212)×(788-212)÷500
=1000×576÷500
=2×576
=1152

Answer 3

用平方差公式a^2-b^2=(a-b)(a+b)
得（5x-y-z)(5y+5z-x)

2a^2(a^2-25b^2)-50b^2(a^2-25b^2) =2(a^2-25b^2)^2
=2(a+5b)^2(a-5b)^2

先提2a,再用平方差公式
得2a(4x^2+8x+1)(4x^2+8x-1)

-x^n[x^4-81(y-z)^2] =-x^n(x^2+9y-9z)(x^2-9y+9z)

（10*14.5+10*5.5）(10*14.5-10*5.5）=200*90=18000

（788-212）（788+212）/500=576*1000/500=1152

Answer 4

1 (-x+5y+5z)(3x-y-z)
2